UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.

A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.

SQUEEZE FLOW OF A SECOND-ORDER FLUID BETWEEN TWO PARALLEL DISKS OR TWO SPHERES

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.

GENERAL SECOND ORDER FLUID FLOW IN A PIPE

It is more satisfactory for fluid materials between viscous and elastic to introducethe fractional calculus approach into the constitutive relationship. This paper employsthe fractional calculus approach to study second fluid flow in a paper. First, we derivethe analytical solution which the derivate order is half and then with the analyticalsolution we verify the reliability of Laplace numerical inversion based on Crumpalgouithm for the problem, and finally we analyze the characteristics of second orderfluid flow in a pipe by using Crump method. The results indicate that the more obviousthe viscoelastic properties of fluid is, the more sensitive the dependence of velocity andstress on fractional derivative order is.

Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.

Three-dimensional channel flow of second grade fluid in rotating frame

An analysis is performed for the hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of a magnetic field. The lower sheet is considered to be a stretching sheet, and the upper sheet is a porous solid plate. By suitable transformations, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. A series of solutions to this coupled non-linear system are obtained by a powerful analytic technique, i.e., the homotopy analysis method （HAM）. The results are presented with graphs. The effects of non-dimensional parameters R, A, M2, a, and K2 on the velocity field are discussed in detail.

Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet

This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method （HAM）. Two-dimensional and axisymmetric shrinking flow cases are discussed.

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.

SECOND-MOMENT CLOSURE FOR MODELLING THE NEAR-WALL TURBULENCE IN 3D MEAN FLOWS

A second-moment closure for the near-wall turbulence is proposed. The limiting behaviour of this closure near a wall is consistent with that of the exact Reynolds-stress transport equations, and it converts asymptotically into a high- Reynolds-number closure remote from the wall. The closure is applied to a pressure- driven 3D transient channel flow. The predicted results are in fair agreement with the DNS data.

Exact analytical solutions for axial flow of a fractional second grade fluid between two coaxial cylinders

The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid,between two infinite coaxial circular cylinders,are determined by applying the Laplace and finite Hankel transforms.Initially the fluid is at rest,and at time t=0^+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions.Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions.The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions.Finally,some characteristics of the motion,as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models,are underlined by graphical illustrations.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 ＋ , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.

不同分数导数下Maxwell杂化纳米流体流动和传热变化的灵敏度分析

研究多孔介质中垂直拉伸板引起的分数阶Maxwell杂化纳米流体流动与传热现象,并考虑二阶滑移边界条件.利用分数阶剪应力和分数阶Fourier定律构建边界层控制方程.然后采用有限差分结合L1算法进行数值求解,并详细讨论分数导数参数增大时,各物理参数对该流体流动与传热影响的灵敏度变化.结果表明,Darcy数和滑移参数对平均表面摩擦系数的影响,以及滑移参数对平均Nusselt数的影响,对速度分数导数比对温度分数导数更敏感.Darcy数对平均Nusselt数的影响只对温度分数导数敏感,与速度分数导数几乎无关.此外,一阶滑移参数比二阶滑移参数对流动和传热的影响更大.

基于二阶锥规划最优潮流计算的主动配电网动态重构研究

为有效应对大规模可再生能源接入电网的不确定性与波动性,实现配网最优运行,提出一种考虑分布式电源时变性与负荷需求特性的动态网络重构优化方法。先针对传统静态支路潮流模型的非凸性,引入松弛变量,将其转化为二阶锥约束,建立基于二阶锥松弛的最优潮流模型;再综合考虑主动配电网环境中的主动管理元素等约束,在保证电压稳定性的前提下,以网络损耗与购电量最小为优化目标,建立高比例分布式电源接入下的多时段配电网重构模型;最后,采用YALMIP工具包和Gurobi求解器进行建模求解,并通过适配IEEE 33节点模型进行实证分析。算例结果表明:所提方案得到的系统期望网络损耗值从0.176 MW减小到0.097 MW,其网络损耗值比粒子群算法的降低了11.95%,其电压水平比粒子群算法的提高了0.76%。该模型的有效性得到了验证。

基于线性化潮流模型的配电网电压无功控制策略

针对现有基于二阶锥松弛的电压无功控制模型无法以电压波动为目标且求解速度较慢等问题,文中提出了一种基于线性化潮流模型的配电网电压无功控制策略。基于支路潮流方程建立了包含有载调压分接头、电容器组和光伏逆变器等调控手段的电压无功控制模型,并将其离散变量松弛为连续变量,以形成二阶锥规划。进一步以二阶锥规划所得结果为基准点构造线性化潮流模型,并以电压波动最小为目标,将连续变量还原为离散变量。最后基于改进的IEEE-33节点测试系统进行了仿真,仿真结果表明所提出的线性化潮流模型具有较高的精度和更快的求解速度,能够适用于配电网实时电压无功控制。

基于分布式新能源与配网网络重构的降损技术

考虑分布式新能源出力随机性对调控策略执行效果的影响,研究了基于电压风险评估和主动重构的日前调度技术。基于光伏出力预测和负荷预测,以电压安全概率风险最小为目标,以开合联络开关为控制变量,应用二阶锥松弛过的Distflow潮流模型进行求解,获取电压安全概率风险最小的配网重构方案。通过对IEEE 33节点配网进行算例分析,仿真结果验证了所提基于电压风险评估与主动重构的日前降损策略的可行性。

考虑交通流量和用户行为不确定性的加氢站选址优化模型

加氢站是氢能产业发展的重要基础设施,其布局选址对于氢能在交通领域的推广应用至关重要。为此,提出一种加氢站的选址优化方法。首先,分别以运营商追求捕获交通流量最大化、客户追求获得加氢服务可能性最大化为上、下层目标函数构建了双层规划模型,并引入机会约束规划理论处理了交通流量的不确定性。该模型考虑了客户路径选择的行为特性,能够为交通流量不确定性下的加氢站选址提供重要借鉴。其次,利用KKT条件和确定性等价将所提机会约束双层规划模型转化为了单层的混合整数二阶锥规划问题以实现高效求解。最后,为验证该模型的有效性,以长三角地区交通网络为案例进行了仿真分析。

计及压缩机运行域的动态最优电-气能流凸化算法

压缩机是电-气互联系统的关键元件,其运行工作点是否位于运行域内关系到系统的安全稳定运行,同时其模型非凸性大幅增加了最优电-气能流的求解难度。为此,该文在压缩机准确建模的基础上,针对电力和天然气系统迥异的传输特性,提出一种计及压缩机运行域的动态最优电-气能流凸化算法。首先,根据压缩机运行参数与状态变量间的映射关系,构建压缩机三维运行域模型,并利用超平面实现运行域的凸包络松弛。其次,考虑差异化传输特性建立动态最优电-气能流模型,实现模型的混合整数二阶锥凸重构,并提出一种基于动态线性化与紧缩凸包络的凸化算法。最后,算例验证所提模型的有效性,表明所提算法在计算精度和效率上均优于连续锥规划算法。

胎盘生长因子联合脐动脉S/D值对子痫前期的预测价值

目的:探讨胎盘生长因子(PLGF)联合脐血流S/D对子痫前期的预测价值。方法:采用病例对照研究,回顾性选取2020年4月—2021年4月就诊于我院产科并最终诊断为子痫前期的孕产妇52例作为研究组,并选取同期正常分娩的产妇122例作为对照组,将孕期划分为三个阶段,孕早期(12~20周)、孕中期(20~34周)、孕晚期(34~42周),收集并分析两组孕妇早中晚期的胎盘生长因子(PLGF)、孕中晚期脐动脉收缩末期最大血流速度(S)与舒张末期最大血流速度(D)比值(S/D),评估PLGF、S/D值单独及联合预测子痫前期的效能。结果:研究组血清PLGF在妊娠各阶段平均值均明显低于对照组(P<0.05),研究组脐动脉S/D平均值高于对照组,孕中期两组间比较差异无统计学意义(P=0.21),孕晚期两组间比较差异有统计学意义(P=0.047),血清PLGF联合脐动脉S/D值在孕中期的特异度、灵敏度、AUC(ROC曲线下面积)分别为80.0%、63.6%、0.664,孕晚期的特异度、灵敏度、AUC分别为71.9%、81.8%、0.804。结论:研究组妊娠各个时期PLGF值均低于对照组,可以单独作为子痫前期患者的预测指标,S/D值单独预测价值与PLGF联合S/D值的预测价值在孕晚期优于孕中期,推测与纳入研究组患者的病情严重程度有关。